The solution to the inequality equations are
a) 15 pt < 2 gal , True
b) 1 gal < 5 qt , True
c) 12 fl oz > 2 c , False
d) 2 qt 1 cup > 2 c , False
e) 20 pints = 10 quarts , True
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
a)
The inequality equation is 15 pt < 2 gal
Now , 15 pints = 1.875 gallons
So , 15 pt < 2 gal is True
b)
The inequality equation is 1 gal < 5 qt
Now , 1 gallon = 4 quarts
So , 1 gal < 5 qt is True
c)
The inequality equation is 12 fl oz > 2 c
Now , 2 c = 16 fl oz
So , 12 fl oz > 2 c is False
d)
The inequality equation is 2 qt 1 cup > 2 c
Now , 2 c = 16 fl oz
So , 2 qt 1 cup > 2 c is False
e)
The inequality equation is 20 pints = 10 quarts
Now , 10 pints = 5 quarts
So , 20 pints = 10 quarts is True
Hence , the inequality equations are solved
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One cylinder has a volume that is 8 Centimeters cubed less than StartFraction 7 over 8 EndFraction of the volume of a second cylinder. If the first cylinder’s volume is 216 Centimeters cubed, what is the correct equation and value of x, the volume of the second cylinder?
StartFraction 7 over 8 EndFraction x + 8 = 216; x = 182 centimeters cubed
StartFraction 7 over 8 EndFraction x minus 8 = 216; x = 196 centimeters cubed
StartFraction 7 over 8 EndFraction x + 8 = 216; x = 238 centimeters cubed
StartFraction 7 over 8 EndFraction x minus 8 = 216; x = 256 centimeters cubed
Answer:
7/8X-8=216
x=256
7/8x-8=216
+8 +8
7/8x=224
7/8 7/8
x=256
Step-by-step explanation:
On Saturday morning, Wendy watched one and a half hours of her favorite shows on television. During the shows there were 15 commercials. What is the unit rate of commercials per hour?
5 hours per commercial
10 commercials per hour
15 commercials per hour
20 commercials per hour
Answer:
10 commercials per hour
Step-by-step explanation:
Hope it helps!
Claire traveled 382 miles. She drove 82 miles every day. On the last day of her trip she only drove 52 miles. Write and solve an equation to find the number of days Claire traveled. Explain each step of your problem solving strategy.
An equation is a mathematical expression that shows the relationship between two variables
How to write and solve an equation to find the number of days Claire traveled.Since Claire traveled 382 miles. She drove 82 miles every day. On the last day of her trip she only drove 52 miles.
Let d represent the number of days Claire travelled.
Since Claire travelled 82 miles per day, the number of miles she travels in d days is D = 82 × d = 82d
Also, since she travels 52 miles on the last day, the total distance she travels is D' = 82d + 52
Now, since the total distance Claire travels is 382 miles, we have that
D' = 382 miles
So,
82d + 52 = 382
So, the required equation is 82d + 52 = 382
Solving the equation for d, we have
82d + 52 = 382
82d = 382 - 52
82d = 330
d = 330/82
d = 4.02 days
d ≅ 4 days
The equation for the number of days Claire travelled is 82d + 52 = 382 The number of days claire travelled is 4 daysLearn more about equation for number of days travelled here:
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write the equation in standard form of the line that has x-intercept -2 and y-intercept 5
Answer: y=(2/5)x +5
Step-by-step explanation:
The vertices of pentagon JKLMN are listed below.
What is the approximate perimeter of the pentagon?
The perimeter of the triangle would be -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}
Given is a pentagon JKLMN .
The perimeter of a figure is the sum of the length of its sides. So, we can write the perimeter of the pentagon as -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}
Therefore, the perimeter of the triangle would be -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}
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A company makes Poppy Lapel pins.
Answer:
the percentage profit of the company is 63.9%.
Step-by-step explanation:
Cost of making pins= £1.10
Number of pins= 1000
Total cost for making the pins
= Cost of each pin × Number of pins
= £1.10 × 1000
= £1110
Percentage of pins sold in charities
= 35% of 1000 pins
= (35/100) × 1000
= 350 pins
Left pins= 1000-350 = 650 pins
Number of pins sold at £3.00:
= 60% of 650
= (60/100) × 650
= 390
Selling price of these 390 pins
= 390 × £3.00
= £1170
Number of pins sold at £5.00 for 2:
= 40% of 650
= (40/100) × 650
= 260
These 260 pins were sold in pairs for £5.
Therefore, number of pairs sold
= 260/2
= 130 pairs
Selling price of these 130 pairs of pins
= 130 × £5.00
= £650
Therefore, total selling price
= £1170 + £650
= £1820
Profit by company
= Selling price - Cost price
= £1820 - £1110
= £710
Profit percentage
= Profit × 100 / Total cost price
= 710 × 100 / 1110
= 71000/1110
= 63.9%
write an equation of a line perpendicular to the line 4x-3y=15 and passes through the point (8 -5)
Answer:
[tex]y+5=-\frac{3}{4}(x-8)[/tex]
Step-by-step explanation:
[tex]4x-3y=15 \\ \\ 3y-4x=-15 \\ \\ 3y=4x-15 \\ \\ y=\frac{4}{3}x-5[/tex]
The slope of the given line is [tex]4/3[/tex]. So, the slope of the line that we need to find is [tex]-3/4[/tex].
Using point-slope form, the equation is [tex]y+5=-\frac{3}{4}(x-8)[/tex].
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!!!!!!!
The number of Cones needed in the first, second, and third cases will be 7, 4, and 3, respectively.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
Let πr³ = x. Then the volume of a cylinder is given as,
V₁ = πr³
V₁ = x
The volume of a sphere is given as,
V₂ = (4/3)πr³
V₂ = 4x/3
The volume of a cone is given as,
V₃ = (1/3)πr³
V₃ = x/3
The number of Cones needed, along with 1 Sphere to equal the volume of one Cylinder will be given as,
⇒ (4x/3 + x) / (x/3)
⇒ (7/3) × (3)
⇒ 7
The number of Cones needed to equal the volume of one Sphere will be given as,
⇒ (4x/3) / (x/3)
⇒ (4/3) × 3
⇒ 4
The number of Cones needed to equal the volume of one Cylinder will be given as,
⇒ (x) / (x/3)
⇒ 1 × 3
⇒ 3
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In a class of 29 students, 18 of them like Maths, 12 of them like English and 7 of them don't like Maths or English. Find the probability that a student chosen at random likes Maths but not English. You may wish to complete the Venn diagram to help you. E
Answer:
34.48%
Step-by-step explanation:
12 + 18 + 7 = 37
37 - 29 = 8
8 students Like both English and Math
Only like math: 18 - 8 = 10
10 / 29 = 34.48%
Answer: 34.48%
Step-by-step explanation: 12 + 18 + 7 = 3737 - 29 = 88 students Like both English and Math. l18 - 8 = 1010 / 29 = 34.48% like math
Functions f(4) determine what f(x)=40
The value of the function at 4, f(4) = 74 and the then value of x when f(x) = 40 is 6.
What are Functions?Functions are defined as the relation between two sets such that elements of a set is mapped to the elements of the other set and no element in the first set has more than one image in the other set.
Given values of x and the function values on those x in the table.
x values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
f values on these x are 60, 64, 42, -5, 74, -4, 40, -29, 3, 47
Clearly we can see that x = 4 maps to 74.
So f(4) = 74.
Similarly we have an f value of 40 at x = 6.
Hence f(4) = 74 and the x = 6 when f(x) = 40.
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In a group of 100 people ; 19 were drinking punch and 23 were eating fish . Find the probability that people picked from this group at random is either drinking punch or eating fish
Probability that people picked from this group at random is either drinking punch or eating fish is 42/100.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Total number of people = 100
Number of people drinking punch = 19
Number of people eating fish = 23
Probability of people drinking punch = 19/100
Probability of people eating fish = 23/100
Probability that people picked from this group at random is either drinking punch or eating fish = P(people drinking punch) + P(people eating fish)
= (19/100) + (23/100)
= 42/100
Hence the probability of people drinking punch or eating fish is 42/100.
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Charlie is at an amusement park that has 18 different rides. Each ride costs $1.75. The function C(r) = 1.75r represents the total amount of money that Charlie will spend if he goes on r rides, but he never goes on the same one more than once. What domain and range are reasonable for the function?
A.
D : 0 ≤ r ≤ 31.5
R : 0 ≤ C(r) ≤ 18
B.
D : 0 ≤ r ≤ 18
R : 18 ≤ C(r) ≤ 31.5
C.
D : 1 ≤ r ≤ 18
R : 1.75 ≤ C(r) ≤ 31.5
D.
D : 0 ≤ r ≤ 18
R : 0 ≤ C(r) ≤ 31.5
Answer:D
Step-by-step explanation:C(r) is how much money it will cost and r is how many rides there are 18 different rides and he won't go on one more than once so the r shoul be less or equalled to 18
if you multiply 1.75 by 18 then it will be 31.5 which means C(r) should be less or equalled to 31.5
he doesn't have to go on a ride so 0 has to be less or equalled to C(r) and r
this means D is correct
Ahmed and Madri Jaleeni are self-employed motel operators.
They pay 100% of the PPO insurance premium of $6,510 annually.
They also have a dental plan that costs $546 annually and a vision
plan that costs $244 annually. The premiums are paid quarterly
(every 3 months). How much do they pay each quarter?
Answer:
$1825 is paid each quarter
Step-by-step explanation:
$6500 for PPO
+ 546 for Dental
+ 244 for vision
= 7300 ÷ 4 (there are 4 quarters in each year)
= $1825 each quarter
In ΔDEF, e = 1.4 cm, f = 9.1 cm and ∠D=109°. Find the area of ΔDEF, to the nearest 10th of a square centimeter.
Answer:
6.0 cm²
Step-by-step explanation:
You want the area of ∆DEF with sides e=1.4 cm, f=9.1 cm, and angle D=109°.
AreaThe area of the triangle is given by the formula ...
A = 1/2ef·sin(D)
A = 1/2(1.4 cm)(9.1 cm)sin(109°) ≈ 6.37·0.94552 cm² ≈ 6.023 cm²
The area of triangle DEF is about 6.0 square centimeters.
Which name is given to a reaction in which the number of each type of atom on one side of the equation is equal to the number of
The same kind of atoms on the other side of the equation?
A balanced
B electrical
C complete
D atomic
Answer:
A balanced
Step-by-step explanation:
A reaction in which the number of each type of atom on one side of the equation is equal to the number of the same kind of atoms on the other side of the equation is called a balanced chemical equation.
It is a chemical equation that has the same number of atoms of each element on both sides of the equation. This is important because the law of conservation of mass states that matter can't be created or destroyed, so the number of atoms on one side of the equation must be equal to the number of atoms on the other side of the equation.
It is also important for calculating the stoichiometry of a reaction, determining the amount of reactants and products needed for a reaction, and to make sure that the chemical equation is in accordance with the laws of thermodynamics.
How many grams of sugar are there in a 200 ml glass of juice?
Apple juice
250 ml contains
Carbohydrate
Sugar
Protein
29.5 g
| 25.5 g
0.3 g
Ans
Answer:
like 10 or 15 grams because theare is glass of juice
200 ml of juice will contain 20.4 g of sugar.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given: 250 ml of juice contains 29.5g carbohydrate, 25.5g sugar , 0.3 g protein.
Now 250 ml of juice contains 25.5 g of sugar
therefore 1 ml of the juice will contain 25.5/250=0.102 g
Thus 200 ml of juice will contain 0.102×200=20.4 g
Hence, 200 ml of juice will contain 20.4 g of sugar.
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please do no spamming 20 points!!!!!!!!!!!!!!!
Answer:
Answer in image
Step-by-step explanation:
Finding the distance between point A and B, then Point C and B will tell you if the two sides are congruent. Then knowing that two sides are congruent, we can determine whether or not the triangle is isosceles, because isosceles triangles have two congruent sides. Then know there are two congruent sides, we know that the base angles must be the same, which leads to the conclusion of this being an isosceles triangle.
-Hope this helped & Happy New Year!
Help me please 50 points please
The area of the triangle JKL is 11/2 units² = 5.5 units².
What are the vertices of a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The coordinates of the vertices of the triangle JKL are J(-2,1), K(0,3), and L(3,-4).
The formula for the area of a triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is A = 1/2[x₁ (y₂ - y₃) + x₂( y₃ - y₁) + x₃ (y₁ - y₂)]
In the question:
x₁ = -2, y₁ = 1, x₂ = 0, y₂ = 3, x₃ = 3, y₃ = -4:
The area of the given triangle is:
A = |1/2[-2 (3 - (-4)) + 0(-4 - 1) + 3(1 - 0)]|
A = |1/2[ -2 × 7 + 0 + 3]|
A = |1/2[ -14 + 3]|
A = |-1/2(11)|
A = 11/2 square units.
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Find the value of r so that the line that passes through the pair of points has the given slope. (2, r) , (4, 2) , m=5/2
Answer:
(2, -3)
Step-by-step explanation:
Write the equation of the line.
y = mx + b We need the slope and the y intercept. We have been give the slope (m) as 5/2. We will use that and the point (4,2) to figure out the y-intercept (b)
m = 5/2
y = 2 from the point given (4,2)
x = 4 from the point given (4,2) Another name for 4 is [tex]\frac{4}{1}[/tex]
y = mx + b substitute in what we know and solve for b
2 = [tex]\frac{5}{2}[/tex][tex](\frac{4}{1})[/tex] + b
2 = [tex]\frac{20}{2}[/tex] + b
2 = 10 + b Subtract 10 from both sides
2 - 10 = 10 - 10 + b
-8 = b
Now that we have the slope (m) (5.2) and the y-intercept (b) -8. We can write the equation of the line.
y = mx + b
y = [tex]\frac{5}{2}[/tex] x - 8
We want to find out what is y when x = 2.
y = [tex]\frac{5}{2}[/tex]x = 8
y = [tex]\frac{5}{2}[/tex](2) - 8
y = 5 - 8
y = -3
In the figure above, c + d = 70.
What is the value of a + b?
From the given figure c+d = 70 and the value of a+b could be 70 .
What is triangle ?
triangle is defined as a plane figure in which it has three sides and three angles.
In the given triangle, in which it contains angle c and d
let another angle could be z .
so c + d + z = 180
as the sum of all three angles in a triangle is 180 degrees.
c+d = 70
so,
z = 180 - (c+d )
z = 180 - 70
z =110
in another traingle which is opposite to angle z.
let angles in that triangle be x , y , f .
x+y+f = 180
180- a + 180 - b + f = 180
180 = a+b+f
angle f = angle z as vertically opposite angles are always equal.
hence
a+b+f = 180
a+b = 180-f
a+b = 180-z
a+b = 180-110
a+b = 70
Hence the value of a+b is 70
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Given (b - 3)(3b + 8)(2b + 5) = 0, which factor(s) must equal zero? J) Only (b - 3) must equal zero. K) Only (3b + 8) must equal zero. L) Only (2b +5) must equal zero. M) At least one factor must equal zero. N) All three factors must equal zero.
M) At least one factor must equal zero.
What are the factors of production?Factors of production are, land, labor, capital, and entrepreneurship
Factors of production is an economic term that describes the inputs that are used in the production of goods or services in order to make an economic profit.
In order for a product of factors to be equal to zero, at least one of the factors must be equal to zero. This is because any number multiplied by zero is equal to zero. So, if (b - 3)(3b + 8)(2b + 5) = 0, then at least one of the factors (b - 3), (3b + 8), or (2b + 5) must equal zero. It is not necessary for all three factors to be equal to zero, as long as one of them is.
Hence, M) At least one factor must equal zero.
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Explain how to determine the zeros of the polynomial f(x)= x³ + (b-a)x² - abx
for the positive real numbers a and b.
The zeros of the polynomial f(x)= x³ + (b-a)x² - abx for the positive real numbers a and b are 0, a, and -b.
What is polynomial?A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.
Given:
f(x) = x³ + (b-a)x² - abx
Take x common on the right side as shown below,
f(x) = x [x² + (b - a)x - ab]
Factorize the term as shown below,
f(x) = x (x - a)(x + b)
Plug the zero on the left side to find the zeros,
0 = x (x - a)(x + b)
x = 0,
x - a = 0,
x = a
x + b = 0,
x = -b
Thus, the zeros are 0, a, and -b.
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round "24.21 16.03 to the nearest whole.number
Answer: 24
Rounded to the nearest 1 or
the Ones Place.
Step-by-step explanation: 24.2116
You rounded to the nearest ones place. The 4 in the ones place rounds down to 4, or stays the same, because the digit to the right in the tenths place is 2.
24
When the digit to the right is less than 5 we round toward 0.
24.2116 was rounded down toward zero to 24
The number 24.21 rounded to the nearest whole number is 24 and the number 16.03 rounded to the nearest whole number is 16
What is rounding up numbers?There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the first number be represented as A
Now , the value of A is A = 24.21
Let the second number be represented as B
The value of B = 16.03
Now , on rounding the number A , we get
You rounded to the nearest ones place. The 4 in the ones place rounds down to 4, or stays the same, because the digit to the right in the tenths place is 2
And , when the digit to the right is less than 5 we round toward 0
So , the rounded number is 24
Now , on rounding the number B , we get
You rounded to the nearest ones place. The 6 in the ones place rounds down to 6, or stays the same, because the digit to the right in the tenths place is 0
And , when the digit to the right is less than 5 we round toward 0
So , the rounded number is 16
Hence , the rounded numbers are 24 and 16 respectively
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Solve the inequality for v.
v + 12>8
Simplify your answer as much as possible.
PLEASEEE HELP ME, I NEED ANSWER ASAP!!!
The simplified inequality is v>-4
What is inequality?An inequality is an inequation separated by <,>≥,≤. In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use the “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given here, the inequality as v + 12>8 simplifying we get
v+12>8
v+12-12>8-12
v>-4
Hence, The simplified inequality is v>-4
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Please HELP! I Need These!
Answer:
(4, 0)
Step-by-step explanation:
A function is a special relation where each input (x-value) has a single output (y-value).
From inspection of the given graph, we can see that the input x = 4 has two outputs: y = 0 and y = -5.
Therefore, for the graph to represent a function, we need to remove one of the points with an input of x = 4:
(4, 0) or (4, -5)the Mary muffin company has 128 peaches they want to bake as many cobblers as they can if it takes nine peaches to make a cobbler how many cobblers will they make how many peaches will not be used
If it takes nine peaches to produce one cobbler and the Mary muffin company has 128 peaches, they want to make as many cobblers as they can. One peach won't be used in the 14-number cobbler that was created.
How many cobblers will they make and peaches will not be used ?If it takes nine peaches to produce one cobbler and the Mary muffin company has 128 peaches, they want to make as many cobblers as they can. They will then produce cobblers that are 128/9 = 14.222. As a result, they will produce 14 varieties of cobblers without using 1 peach. It is derived by dividing the share price of a corporation by the number of outstanding shares, as opposed to book value or shareholders' equity, which is only the difference between a firm's assets and liabilities. The simplest approach of valuing a company is market capitalization.It is computed by dividing the share price of the corporation by the total number of outstanding shares. Market capitalization is a frequent illustration of valuation. This multiplies a company's share price by the total number of outstanding shares.To learn more about Mary muffin company refer to :
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What is the remainder when 3 is synthetically divided into the polynomial
-2x² + 7x-9?
A. -6
B. 0
C. -4
D. 2
Answer:
A. -6 is the correct answer.
Answer:
So the remainder when 3 is synthetically divided into the polynomial -2x² + 7x - 9 is -6. The correct answer is therefore A.
(6+3)²+(9-10+5) what’s the answer
Answer:
15 + 4
Step-by-step explanation:
#15 At Greenville Middle School, students are enrolled in a foreign
language. Use the table to answer the following question: What
percentage of 7th graders are enrolled in French or German?
The percent value of 7th grade students enrolled in French or German is given as 64%.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
As per the table given the following data can be concluded as,
Total number of students in 7th grade is 11 + 13 + 5 + 15 = 44
And, the number of students of 7th grade in french or german is,
Number of students in French + Number of students in German
⇒ 13 + 15 = 28
Then, the percent value can be calculated by the operation given below as,
⇒ 28 ÷ 44 × 100 = 63.63%
Which is approximately 64%.
Hence, the percent value of 7th graders in French or German is obtained as 64%.
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3000/7.333333 to a whole number
The whole number for the given rational number is 409.
What is a whole number?Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.
Given that, 3000/7.333333.
Here, take x=7.3333...... ------(I)
Multiply equation (I) by 10, we get
10x=73.3333...... ------(II)
Subtract equation (I) from equation (II), we get
9x=66
x=66/9
x=22/3
Now, 3000÷22/3
3000×3/22
= 9000/22
= 409
Therefore, the whole number for the given rational number is 409.
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